Is There a Breast Lift Technique That Does Not Involve Moving the Nipple?

Depending on your exact anatomy, there may be additional skin tightening options, but to explore them will require a set of photographs at minimum, and direct examination and measurements optimally.

The least number and degree of scars that can achieve your goals is the best plan, but loose skin requires skin removal and scars, in many cases around the nipple/areola complex in order to raise its position properly atop the tightened skin brassiere. BTW, a scar around your areola does NOT mean that it was detached and reattached as a skin graft; in fact, the opposite is true in the majority of cases! The nipple/areola complex is left attached to the glandular tissues, preserving sensation and ability to breast-feed in a majority of patients. Detachment and grafting is necessary only in rare cases, and will result in anesthetic (numb) and non-functional (ability to breast feed) nipples when this is done.

Tailoring your skin excisions and scars to your exact anatomic needs and goals will give you the results that will be the best cosmetically, and least likely to require revision.

See one of more American Board of Plastic Surgery-certified plastic surgeons who do lots of breast surgery and see what your options are. Best wishes!

It's difficult to answer a specific question about your breasts without photos.  In general given your breast size, it is unlikely that a lift could be done without making an incision around the areola, removing the excess tissue, and redraping the remaining skin and breast tissue around the nipple into a pleasing contour.   If all of the extra breast tissue and skin is below the nipple (and the nipple is in good position) it may be possible to remove it with just an incision in the fold, but again, this is not the most likely situation.